%& .-1$# 30 ) 9 k30 l11 k30...a] x a(1)
TRANSCRIPT
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1
( ) 30 9 30 11 30
1. 2 A B 4 A, B, C, D2 A B 2 A B 4
10 2 3
[
2. 1 4 ([1] [2] ) 44 1 2
4 3
3. 4 1 24 4
4. ( A B ) ([1] [2] )
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A (100 )
[ 1 ] [ 4 ]
[ 1 ] (25 ) 3× 3 M a, b
M =
⎡
⎢⎢⎣
1 b 3
a 3 6
3 6 9
⎤
⎥⎥⎦ .
(1) (3)
(1) a = 2, b = 0 M r M
r
(2) a, b M 1
(3) a = b M det(M) a
M a
[ 2 ] (25 ) n n Rn
W W W⊥
W⊥ = {y ∈ Rn | yTx = 0 (∀x ∈ W )}.
yTx x y (1) (2)
(1) W W⊥
(2) W W⊥ 1 W
x1,x2, . . . ,xr W⊥ y1,y2, . . . ,ys r, s
{x1,x2, . . . ,xr,y1,y2, . . . ,ys}
(1)
[ 3 ], [ 4 ]
2
-
[ 3 ] (25 ) (1) (2)
(1) f : Rn → R x̄ ∈ Rn d ∈ Rn
limt→+0
f(x̄+ td)− f(x̄)t
f : R2 → R
f(x1, x2) =
⎧⎨
⎩
(x1 + x2)(x1 − x2)2
(x1 + x2)4 + (x1 − x2)2((x1, x2) ̸= (0, 0)
),
0((x1, x2) = (0, 0)
),
(d1, d2)
(2) g : R → R 3∫ 2
0g(x) dx
g(0), g(1), g(2)
[ 4 ] (25 ) y x (A)
d2y
dx2+ 2
dy
dx+ y = 0
(1) (3)
(1) y = eαx (A) α
(2) y = xeβx (A) β
(3) (A)
3
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B (100 )
[ 1 ], [ 2 ]
[ 1 ] (50 ) (1) (2)
(1) A B f A P f P
f(P ) = {b ∈ B | a ∈ P, f(a) = b}
{ }
a ∈ P f(a) ∈ f(P )
⎧⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎩
⎫⎪⎪⎪⎪⎬
⎪⎪⎪⎪⎭
(2) R f : R → R x, y ∈ R α ∈ [0, 1]
f((1− α)x+ αy) ≤ (1− α)f(x) + αf(y).
f x ∈ R
f(x) = x2 − 2x
f
[ 2 ]
4
-
[ 2 ] (50 ) (1) (2)
(1) X Y (a)
(c)
Y
X 1 2 3
0 1/8 0 0
1 0 2/8 1/8
2 0 2/8 1/8
3 1/8 0 0
(a) X Y
(b) X Y
(c) X Y
(2) X (Poisson)
P (x) =exp(−λ)λx
x!, x = 0, 1, 2, . . .
(a) (b)
(a) X ( )
(b) n (X1, X2, . . . , Xn)
λ
5
-
6
A 100 [ ] [ ]
[ ]
L x
2 21 1( , ) 2 ( ) 22 2
u R x R x x L L x x= + - = - + -
R L 3
(1) w x 1 2L =
2x wR w+ = 0 2R£ £ 0x ³
x ( )x w ( )R w
R x 4 1/2w = 1w = 2w =5
( )L w
4 4 [ 5
4 4
R x 4
[ ]
-
7
( ! "#, "% =min "#, "% "# "%
* = max - − /0, 0 0* - /
3 4(3)7# > 0 7% > 0
4
-
B (100 )
[ 1 ]
[ 1 ] (100 )
t(= 1, 2, . . .)
t
• iBct−1Mt −Mt−1 Bct −Bct−1 Bct Mt
t i > 0
• St iBct−1Bgt −B
gt−1 Gt iB
gt−1 B
gt
t
(1) (3)
(1) Bt ≡ Bgt − Bct2
Bt −Bt−1 +Mt −Mt−1 + St = iBt−1 +Gt.
(2) t GDP yt pt
ytyt−1
= γ,ptpt−1
= π.
γ > 1 GDP π π > 1
π < 1
r
r =1 + i
π− 1
π < 1 + i r > 0
8
-
bt ≡Btptyt
, mt ≡Mtptyt
, gt ≡Gtptyt
, st ≡Stptyt
.
(1)
bt +mt =1 + r
γbt−1 +
1
πγmt−1 + gt − st.
(3)
t g < s+ b+m
(g − s > 0) m > 0
g − s > 0 b
9
-
C (100 )
[ 1 ], [ 2 ]
[ 1 ] (50 )
Yi = α+ βXi + ϵi, i = 1, 2, . . . , n
Xi E(ϵi) = 0, V ar(ϵi) = σ2, Cov(ϵi, ϵj) = 0 (i ̸= j)(1) (4)
(1) β β̂ = c0 +∑n
i=1 ciYi
c0, c1, . . . , cn β̂
(2) β̂
(3) wi =Xi−X̄∑n
j=1(Xj−X̄)2β b b =
∑ni=1wiYi
X̄ = 1n∑n
i=1Xi c0, c1, . . . , cn (1)
di = ci − win∑
i=1
diwi = 0
(4) β b
[ 2 ]
10
-
[ 2 ] (50 )
Y = X1β1 +X2β2 + ϵ, E[ϵ] = 0, E[ϵϵ′] = σ2In
Y n× 1 X1 n× k1 X2 n× k2β1 k1 × 1 β2 k2 × 1 ϵ n× 1In n× n (1) (4)
(1) X2 Y X1
β1 β1
(2) Y X1 β1 b1 b1
(3) b1 β1
(4) β2 = 0 Y X1 X2 β1
11
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12
D 100 [ ] [ ]
[ ] 50
(1) (4)
X Y
X 2, a 3, b
Y 0, c 4, d
(1) a, b, c, d (2) 4 4
(1) 4 [
(3) 3 9 β 3 9 :3 ; 0 < ; < ; ;
3 1 − ; > 9, 9 + ;> 9, : > 1 − ; > :, 9 + ;>(:, :)
> 9, : 9 :9 β 3
3 (9, 9) 3 > 9, 9 = > :, 9 : > 9, : > > :, :
(4) (2) [ 4 4 4 β
3 (3) 4
[ ]
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13
[ ] 50 3 1 2 3, ,r r r4 E 4 4
( ) max{ ,0}ii N Sv S E rÎ -= -å ( , )S N SÍ ¹Æ ( ) 0v Æ = {1,2,3}N = 3 4
i 0ix ³
1 2 310, 20, 30r r r= = =
(1) 10E = 1 2 3, ,x x x 103
1x 2x
3x 4 3
(2) 20E = 1 2 3, ,x x x 203
(3) 45E = 1 2 3, ,x x x 453
(4) 10E = 20E = 45E = (1), (2), (3) 4
(5) 10E = 20E = 45E = (1), (2), (3) 4
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14
A 100 [ ] [ ]
[ ] 50 X 4 1 1
5 4 1
D B 1 6
(1) (4)
1 X
1 2 3 4 5 6 7 8 9 10
200 100 200 300 400 250 100 100 250 100
1 X
1 2 4 X MRP X
500 2 ]
4
2 MRP
1 2 3 4 5 6 7 8 9 10
]
X(1)
C(2)
C(3) B(2) A(1)
D(6)
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15
2 A X C X 3
A 3 2 4 A
C MRP A 300
100 1 ] 4
C 1500 2 ]
600 300
2
3 4 X 4 3
200 1 50,000
1 1 3 125 3
4
4 MRP JIT MRP
4 [
[ ]
-
16
[ ] 25 3 42 4 3
4 4 (1) (3)
2
3
4
4
(1) 17 17
4 4 4
{
4
}
-
17
(2) (3) (2) 5
β 4 4
[ ] 25 3 ATM 4(1) (3)
(1) 4
{
}
(2) ATM [ 54 5 ATM 4
5 [
[
(3) 4 ATM4 4
4 [
4
ATM
4
5
-
B (100 )
[ 1 ], [ 2 ]
[ 1 ] (50 ) n c,a ∈ Rn+ b ∈ R+
P: max. c⊤x s. t. a⊤x ≤ b, 0 ≤ x ≤ 1
. λ ,
P(λ): max. c⊤x+ λ(b− a⊤x) s. t. 0 ≤ x ≤ 1
, f(λ) . (1) (5) .
(1) n = 3, c⊤ = (3, 4, 6), a⊤ = (2, 5, 10), b = 10 P
. ( ) ,
.
(2) n = 3, c⊤ = (3, 4, 6), a⊤ = (2, 5, 10), b = 10 P(1)
f(1) . ( ) ,
.
(3) n = 3, c⊤ = (3, 4, 6), a⊤ = (2, 5, 10), b = 10 y = f(λ)
, λ ∈ [0, 2](4) λ , f(λ) P .
(5) λ , f(λ) .
[ 2 ]
18
-
[ 2 ] (50 ) 70
86.0 146.3 106.9 147.2 107.9 62.1 147.4 52.0 122.9 83.3
104.9 68.8 87.0 117.0 69.5 185.0 45.2 105.8 108.8 60.9
83.2 47.5 156.4 136.3 95.8 112.1 32.8 37.1 94.1 78.1
20.6 135.2 80.8 119.1 55.8 76.3 58.3 98.9 146.4 135.0
160.4 99.1 114.2 66.9 64.5 87.4 56.1 90.3 59.5 118.2
50.4 87.6 54.6 87.1 78.0 47.1 81.5 36.9 114.6 152.4
95.7 44.6 86.1 63.1 149.5 110.0 89.2 47.2 90.0 93.1
( 100 )
19
-
20
A 100 [ ] [ ]
[ ] 40 PPM5 45
3 (1) (4) (1) PPM 4 3 1BCG
2 0
4 (2) 5 4
[ 4 4 [ (3) 5
4 [ 4 4
[ (4) 5
4 (1) 53 3
5 [
[ ] 30 (1) (2) (1)
3 4(a) (b) (a) 4 (b) (a) [
4 4 4
4 4
(2) 4 4(a) (c)
(a) 4 (b) 4
[ (c)
4 [
[ ]
-
21
[ ] 30 ] 3 ]5 3
] a h 8
8 ] 5
a f b 3 a c e 4
3 b d g 3 4 a f 3 f 3 a b C c d S e O f A g h I 3
(1) (3)
(1) a h ] 43 [
5 [ 4 4 (2) 4 4 ] 3 5
0 4 [ (3) O A I e f g h
5 ]
] 4 4
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22
B 100 [ ] [ ]
[ ] 50 TOKO TOKO 20X5 , 20X6 , 20X7
4 4 , (1)
(5) , 4 4
4 4
TOKO
20X5 20X6 20X7
1,000 800 1,100
400 320 440
200 160 220
320 320 320
40 40 40
(1) 20X5 (%) (2) 20X5 20X6 , 20X7 500
460 , 540 3 20X7 (%)
(3) TOKO (4) TOKO
5
(5) (4) 3 [,
[ ],[ ]
-
23
[ ] 20 (1) (2) 4
2
(1) 3
100
2% 1 4
4
2
4%
(2) 1 3% 2
4% 1 2 %
5 4
[ ] 20 CAPM 4 (1) (2)
4
2
(1) 20XX 1% TOPIX
6% 20%
A TOPIX 0.05 B TOPIX
0.03 A B Y
X ) A B
Y (%)
(2) 4 C ]
) 0.8 C 5
30% ) 0.05
C 30% )
[ ]
-
24
[ ] 10 D D
4 D 4 MBO (Management Buyout)
5 4 M&A